Geodesic
Semi-Free Actions with Manifold Orbit Spaces
Documenta mathematica, Tome 25 (2020), pp. 2085-2114
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

In this paper, we study smooth, semi-free actions on closed, smooth, simply connected manifolds, such that the orbit space is a smoothable manifold. We show that the only simply connected 5-manifolds admitting a smooth, semi-free circle action with fixed-point components of codimension 4 are connected sums of S3-bundles over S2. Furthermore, the Betti numbers of the 5-manifolds and of the quotient 4-manifolds are related by a simple formula involving the number of fixed-point components. We also investigate semi-free S3 actions on simply connected 8-manifolds with quotient a 5-manifold and show, in particular, that there are strong restrictions on the topology of the 8-manifold.
DOI : 10.4171/dm/794
Classification : 55R55, 57K50, 57S17
Mots-clés : circle action, semi-free action, 5-manifolds, 4-manifolds, 8-manifolds 
@article{10_4171_dm_794,
     author = {John Harvey and Martin Kerin and Krishnan Shankar},
     title = {Semi-Free {Actions} with {Manifold} {Orbit} {Spaces}},
     journal = {Documenta mathematica},
     pages = {2085--2114},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/794},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/794/}
}
TY  - JOUR
AU  - John Harvey
AU  - Martin Kerin
AU  - Krishnan Shankar
TI  - Semi-Free Actions with Manifold Orbit Spaces
JO  - Documenta mathematica
PY  - 2020
SP  - 2085
EP  - 2114
VL  - 25
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/794/
DO  - 10.4171/dm/794
ID  - 10_4171_dm_794
ER  - 
%0 Journal Article
%A John Harvey
%A Martin Kerin
%A Krishnan Shankar
%T Semi-Free Actions with Manifold Orbit Spaces
%J Documenta mathematica
%D 2020
%P 2085-2114
%V 25
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/794/
%R 10.4171/dm/794
%F 10_4171_dm_794
John Harvey; Martin Kerin; Krishnan Shankar. Semi-Free Actions with Manifold Orbit Spaces. Documenta mathematica, Tome 25 (2020), pp. 2085-2114. doi: 10.4171/dm/794

Cité par Sources :